Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1854 - 432 páginas |
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Página 17
... theorem is a truth which becomes evident by means of a demonstration . 4. A problem is a question proposed , which requires a solution . 5. A lemma is a subsidiary truth , employed for the demonstration of a theorem , or the solution of ...
... theorem is a truth which becomes evident by means of a demonstration . 4. A problem is a question proposed , which requires a solution . 5. A lemma is a subsidiary truth , employed for the demonstration of a theorem , or the solution of ...
Página 20
... the line , or at a point of a line . 7. That a straight line may be drawn , making with a given straight line , an angle equal to a given angle . PROPOSITION I. THEOREM . If one straight line meet another 20 GEOMETRY .
... the line , or at a point of a line . 7. That a straight line may be drawn , making with a given straight line , an angle equal to a given angle . PROPOSITION I. THEOREM . If one straight line meet another 20 GEOMETRY .
Página 21
... THEOREM . If one straight line meet another straight line , the sum of the two adjacent angles will be equal to two right angles . Let the straight line DC meet the straight line AB at C ; then will the angle ACD plus the angle DCB , be ...
... THEOREM . If one straight line meet another straight line , the sum of the two adjacent angles will be equal to two right angles . Let the straight line DC meet the straight line AB at C ; then will the angle ACD plus the angle DCB , be ...
Página 22
... THEOREM . Two straight lines , which have two points common , coincide the one with the other , throughout their whole extent , and form one and the same straight line . Let A and B be the two common points of two straight lines . In ...
... THEOREM . Two straight lines , which have two points common , coincide the one with the other , throughout their whole extent , and form one and the same straight line . Let A and B be the two common points of two straight lines . In ...
Página 24
... THEOREM . If two triangles have two sides and the included angle of the one , equal to two sides and the included angle of the other , each to each , the two triangles will be equal . In the two triangles EDF and BAC , let the side ED ...
... THEOREM . If two triangles have two sides and the included angle of the one , equal to two sides and the included angle of the other , each to each , the two triangles will be equal . In the two triangles EDF and BAC , let the side ED ...
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Términos y frases comunes
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Pasajes populares
Página 27 - If two triangles have two sides of the one equal to two sides of the...
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Página 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 26 - The sum of any two sides of a triangle is greater than the third side.
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 93 - The area of a parallelogram is equal to the product of its base and altitude.
Página 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 323 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.